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A Common Framework for Developing Robust Power-Flow Methods with High Convergence Rate
(MDPI, 2021-07) Tostado-Véliz, Marcos; Kamel, Salah; Escámez-Álvarez, Antonio; Vera-Candeas, David; Jurado-Melguizo, Francisco
This paper presents a novel Power-Flow solution paradigm based on the structure of the members of the Runge–Kutta family. Solution approaches based on the introduced solution paradigm are intrinsically robust and can achieve high-order convergences rates. It is demonstrated that some well-known Power-Flow solution methods are in fact special cases of the developed framework. Explicit and embedded formulations are discussed, and two novel solution methodologies based on the Explicit Heun and Embedded Heun–Euler’s methods are developed. The introduced solution techniques are validated in the EU PEGASE systems, considering different starting points and loading levels. Results show that the developed methods are quite reliable and efficient, outperforming other robust and standard methodologies. On the basis of the results obtained, we can affirm that the introduced solution paradigm constitutes a promising framework for developing novel Power-Flow solution techniques.
A comprehensive electrical-gas-hydrogen Microgrid model for energy management applications
(Elsevier, 2021-01) Tostado-Véliz, Marcos; Arévalo, Paul; Jurado-Melguizo, Francisco
Recently, a growing interest on multienergy Microgrids has been observed. This kind of grids involves different energy vectors and treat them on a whole. The most typical cases contemplate electrical, natural gas and hydrogen subsystems. Multiple efforts have been conducted on modelling this kind of grids for energy management problems. However, it is observed that most of references studied do not faithfully modelling this kind of grids or directly omit some of the mentioned subsystems, which difficults the accurately representation of these grids. This paper aims at developing a comprehensive but tractable yet multienergy MG model, which allows to accurately represent the interaction between electrical, natural gas and hydrogen subsystems. To that end, the developed framework includes detailed models of the different elements which are typically encountered in this kind of grids such as Gas-to-Power or Power-to-Gas facilities. Also, charging stations for electrical, natural gas and hydrogen vehicles are considered. Different tariffs and vehicle charging modes can be easily incorporated within the developed framework. The proposed model is validated with a case study in typical winter and summer scenarios based on real data. Results show that the developed model is able to accurately represent the operational behavior of multienergy Microgrids, which may be valuable for multiple research and educational tools.
A data-driven methodology to design user-friendly tariffs in energy communities
(Elsevier, 2024-03) Tlenshiyeva, Akmaral; Tostado-Véliz, Marcos; Hasanien, Hany M.; Khosravi, Nima; Jurado-Melguizo, Francisco
In recent years, energy communities have emerged as a feasible solution to empower domestic end-users to engage in local power trading with their neighbours, in an attempt to improve the efficiency and economy of residential consumers. From a mercantilist point of view, launching local markets with eventual local electricity prices might be beneficial for community users as they are inhibited from external volatile prices and possible market imperfections. However, local pricing strategies should take into account users’ preferences and avoid undesirable effects of response fatigue (i.e. excessive number of response signals within a short-time period). This way, local electricity tariffs should be stable and send coherent response signals easily interpretable by users. In this sense, the necessity of developing proper designing tools for local electricity tariffs is clear. This paper focuses on this issue. In particular, the main novelties of this paper are twofold: on the one hand, the developed tool designs community tariffs over a year basis instead of daily spot prices, as made in existing approaches. Thereby, the resulting tariff keeps stable yearly similar to conventional tariffs offered by retailers worldwide. Secondly, the designed tariff takes into account the negative effects of response fatigue, so that the considered pricing mechanism limits the number of pricing signals sent to consumers, taking this feature as an external parameter. This way, the designer is able to tune up the total number of pricing signals that users received within a time period, thus ensuring that they are not discouraged to partake in the community. The proposed design approach is raised as a data-driven framework, taking advantage of real databases collecting demand, renewable generation and retailer prices. Such profiles serve as inputs for a designed bi-level Stackelberg-based problem, in which the reaction of prosumers is implicitly assumed. A case study is conducted on a benchmark energy community. Different tariff mechanisms are analysed such as flat, time-of-use and happy hours tariffs. The results obtained serve to validate the new proposal as well as analyse the effect of local market mechanisms in energy communities.
A four-stage framework for optimal scheduling strategy of smart prosumers with vehicle-to-home capability under real time pricing based on interval optimization
(Wiley, 2023-09) Tostado-Véliz, Marcos; Ghadimi, Ali Asghar; Miveh, Mohammad Reza; Myyas, Ra'ed Nahar; Jurado-Melguizo, Francisco
With the emergence of the Smart Grid concept, utility companies require more active participation of home users in the power sector. This changing paradigm is enabled by the wide deployment of multiple home assets such as small renewable-based generators or storage facilities. In this context, consumers are no longer conceived as pure loads but also active agents that can exchange energy with the grid. To promote this active participation, utility companies promote different price-based demand response programs to change the consumer patterns on pursuing a more efficient and economic system operation. In this regard, home energy management programs are becoming an essential tool for efficiently managing the different home users while addressing multiple demand response goals at minimum cost. In essence, a home energy management system is a computational optimization tool, which has to handle multiple uncertainties brought by weather forecast or energy pricing. This paper tackles this issue by developing a novel robust home energy management program based on interval optimization. In contrast to other related approaches, the proposal avoids the explicit use of interval arithmetic. Instead, the different uncertain parameters are sequentially incorporated into the scheduling task through different stages and interval-based formulation. The developed methodology incorporates weather, load, energy pricing and plug-in electric vehicle related uncertainties. A benchmark case study in a smart prosumer layout serves to prove the effectiveness of the new approach.
A hybrid intelligent model to predict the hydrogen concentration in the producer gas from a downdraft gasifier
(ELSEVIER, 2022-06-05) Aguado-Molina, Roque; Casteleiro-Roca, José Luis; Vera, David; Calvo-Rolle, José Luis
This research work presents an artificial intelligence approach to predicting the hydrogen concentration in the producer gas from biomass gasification. An experimental gasification plant consisting of an air-blown downdraft fixed-bed gasifier fueled with exhausted olive pomace pellets and a producer gas conditioning unit was used to collect the whole dataset. During an extensive experimental campaign, the producer gas volumetric composition was measured and recorded with a portable syngas analyzer at a constant time step of 10 seconds. The resulting dataset comprises nearly 75 hours of plant operation in total. A hybrid intelligent model was developed with the aim of performing fault detection in measuring the hydrogen concentration in the producer gas and still provide reliable values in the event of malfunction. The best performing hybrid model comprises six local internal submodels that combine artificial neural networks and support vector machines for regression. The results are remarkably satisfactory, with a mean absolute prediction error of only 0.134% by volume. Accordingly, the developed model could be used as a virtual sensor to support or even avoid the need for a real sensor that is specific for measuring the hydrogen concentration in the producer gas.
A local electricity market mechanism for flexibility provision in industrial parks involving Heterogenous flexible loads
(Elsevier, 2024-04) Turdybek, Balgynbek; Tostado-Véliz, Marcos; Mansouri, Seyed Amir; Jordehi, Ahmad Rezaee; Jurado-Melguizo, Francisco
Industrial parks allow industries to share infrastructure and thus saving money, finally redounding in improving the economy of many countries worldwide. Given the objectives of carbon neutrality imposed by different entities, it results mandatory promoting energy efficiency in industrial parks. Aligning with such objective, encouraging industries to provide energy flexibility becomes essential. In the electricity sector, such flexibility can be provided through optimally managing local assets such as energy storage and flexible loads. However, flexibility provision should be promoted by implanting proper pricing mechanisms. This paper focuses on this issue by developing a local market clearing mechanism for industrial parks, whose main novelty redounds in the inclusion of a fair pricing mechanism through which industries are paid by flexibility provision. Different types of flexible loads are considered and modelled (i.e. curtailable, interruptible and deferrable), so that the new proposal is suitable for leveraging fully capabilities of industrial flexible loads. The whole pricing mechanism is raised as a bi-level game-based model, by which local energy and flexibility prices are revealed in a coordinated way. Challenges brought by the inclusion of binary variables (needed for modelling some types of flexible loads) are solved by proposing a solution algorithm based on the well-known Column & Constraint Generation Algorithm. The resulting optimization framework is Mixed Integer Linear Programming, being therefore solvable by off-the-shelf solvers. A case study is presented to validate the new proposal as well as highlight some important aspects related to local markets in industrial parks and its practical implantation.
A MILP framework for electricity tariff-choosing decision process in smart homes considering ‘Happy Hours’ tariffs
(Elsevier, 2021-10) Tostado-Véliz, Marcos; Mouassa, Souhil; Jurado-Melguizo, Francisco
Nowadays, electricity end users can choose among a huge variety of different electricity plans on a deregulated energy market. The wide variety of tariffs besides the advent of novel agents like smart consumers and prosumers, are becoming the tariff-choosing process more complex. This paper proposes a MILP optimization framework which aims at facilitating this task. More precisely, the main endings of the developed framework are: (i) determine the most suitable tariff for smart consumers and prosumers based on historical consumption data, (ii) determine the optimal hours to be hired for a so-called ‘Happy hours’ tariff plan. In addition, other useful results can be directly obtained from the developed tool. The developed approach carries out a MILP optimization framework for optimal scheduling a series of flexible appliances through various characteristic days obtained from clustering historical collected data. This process is repeatedly executed for the different tariff options and, finally, the most attractive one is selected. A case study on the Spanish retail market for a benchmark prosumer environment is used for showing the capabilities of the developed framework.
A mixed-integer-linear-logical programming interval-based model for optimal scheduling of isolated microgrids with green hydrogen-based storage considering demand response
(Elsevier, 2022-04) Tostado-Véliz, Marcos; Kamel, Salah; Hasanien, Hany; Turky, Rania; Jurado-Melguizo, Francisco
Hydrogen produced from renewable sources (green hydrogen) will be recognized as one of the main trends in future decarbonized energy systems. Green hydrogen can be effectively stored from surplus renewable energy to thus reducing dependency of fossil fuels. As it is entirely produced from renewable sources, green hydrogen generation is strongly affected by intermittent behaviour of renewable generators. In this context, proper uncertain modelling becomes essential for adequately management of this energy carrier. This paper deals with this issue, more precisely, a novel optimal scheduling model for robust optimal scheduling of isolated microgrids is developed. The proposal encompasses a green hydrogen-based storage system and various demand-response programs. Logical rules are incorporated into the conventional optimal scheduling tool for modelling green hydrogen production, while uncertain character of weather and demand parameters is added via interval-based formulation and iterative solution procedure. The developed tool allows to perform the scheduling plan under pessimistic or optimistic point of views, depending on the influence assumed by uncertainties in the objective function. A case study serves to validate the model and highlight the paper of green hydrogen-based storage facilities in reducing fossil fuel consumptions and further exploit renewable sources.
A new approach based on economic profitability to sizing the photovoltaic generator in self-consumption systems without storage
(Elsevier, 2020-04) Jiménez-Castillo, Gabino; Muñoz-Rodriguez, Francisco José; Rus-Casas, Catalina; López-Talavera, Diego
A proper assessment of the cost-competitiveness and profitability of self-consumption systems is crucial to promoting the transition from grid-dependent to energy self-sufficient buildings. Most of the approaches found in the literature may not take into account economic parameters such as taxes, depreciation and the cost of financing, which have a significant effect on the economic profitability of an investment. Moreover, they only focus on discrete array powers and relatively high recording intervals when estimating the self-consumed energy. In order to manage the aforementioned challenges, a new method will be developed to size the PV generator in a PV self-consumption system which provides the NPV curve together with the self-consumption and self-sufficiency indices for a wide range of array powers which suits residential self-consumption systems. Two scenarios will be considered depending on whether the generated surplus electricity is wasted or it is remunerated from the grid operator. Results show that not only the chosen scenario but the electricity tariff may be key parameters when optimizing NPV. Furthermore, the impact of the recording interval may be significant when estimating NPV. Percentage errors of 11.4% and 33.6% may be reached when considering a recording interval of 15 and 60 min, respectively.
A new approach to analyse from monitored data the performance, matching capability and grid usage of large Rooftop Photovoltaic systems. Case of study: Photovoltaic system of 1.05 MW installed at the campus of University of Jaén
(Elsevier, 2025) Muñoz-Rodríguez, Francisco José; Gómez-Vidal, Pedro; Fernández-Carrasco, Juan Ignacio; Tina, Giuseppe Marco; Jiménez-Castillo, Gabino
Rooftop photovoltaic installations highlight their potential to meet a significant portion of urban electricity demand. These systems range from a few kW in residential areas to hundreds of kW in large Rooftop PV systems in commercial and industrial settings. The latter, which may include several inverters or arrays with different orientations and inclinations, require a proper analysis to assess the potential of this technology and to ensure the design objectives. This paper presents a methodology for analysing from monitored data large Rooftop PV systems, focusing on performance, self-consumption and grid usage. The approach is scalable, applicable at the inverter, individual Rooftop PV and global system levels. New key parameters defined include weighted system irradiation (HI,weighted) and weighted system reference yield (Yr,weighted), which account for different array orientations and inclinations. The methodology is validated using a 1.05 MW system at the University of Jaén with monitored data over a year. Results indicate subsystem and system PR values above 0.83 and a system Capacity Factor of 0.19, confirming a proper performance. Annual self-consumption and self-sufficiency indices of 97.5 % and 17.7 %, respectively, and a solar hour self-sufficiency of 27.7 % reveal minimal energy export and substantial potential to meet the university’s electricity demand.
A new approach to sizing the photovoltaic generator in self-consumption systems based on cost–competitiveness, maximizing direct self-consumption
(Elsevier, 2019-01) López-Talavera , Diego; Muñoz-Rodríguez , Francisco José; Jiménez-Castillo, Gabino; Rus-Casas, Catalina
Applications for sizing Photovoltaic (PV) self-consumption systems have been studied over recent years in order to achieve either an optimization of the cost of energy, the investment cost or any economic profitability criteria. However, PV self-consumption systems at the residential or small business level can be designed with the aims of reducing the electricity consumption from the conventional local grid and achieving competitiveness with grid electricity prices. These criteria will provide not only greater environmental benefits, security and independence of the grid but it will make the cost of PV self-consumption electricity competitive with electricity prices from the power grid. In this sense, this paper proposes a method to size the generator for a PV self-consumption system based on cost-competitiveness, maximizing direct self-consumption. The method will be applied for three different households located in the south of Spain using the household daily consumption and generation profiles for a single year. However, the method here illustrated can be applied to other countries. The results obtained suggest that residential direct PV self-consumption systems with an annual global irradiation at the optimal tilt angle higher than 1000 kWh/(m2·year) may be a feasible investment to future owners of these systems.
A New Methodology for Smoothing Power Peaks Produced by Electricity Demand and a Hydrokinetic Turbine for a Household Load on Grid Using Supercapacitors
(MDPI, 2021-11) Arévalo, Paul; Tostado-Véliz, Marcos; Jurado-Melguizo, Francisco
The power fluctuations produced by electric vehicles represent a drawback in large-scale residential applications. In addition to that, short power peaks could pose a risk to the stability of the electrical grid. For this reason, this study presents a feasibility analysis for a residential system composed of electric vehicle chargers. The objective is focused on smoothing the power fluctuations produced by the charge by a supercapacitor through adequate energy control; in addition, self-consumption is analyzed. Data sampling intervals are also analyzed; the modeling was performed in Matlab software. The results show that there are errors of up to 9% if the data are measured at different sampling intervals. On the other hand, if the supercapacitor is considered, the system saves 59.87% of the energy purchased from the utility grid per day, and the self-consumption of electricity by prosumers can increase up to 73%. Finally, the hydrokinetic/supercapacitor/grid system would save up to 489.1 USD/year in the cost of purchasing electricity from the grid and would increase by 492.75 USD/year for the sale electricity.
A new tool to analysing photovoltaic self-consumption systems with batteries
(Elsevier, 2021-05) Muñoz-Rodríguez, Francisco José; Jiménez-Castillo, Gabino; de-la-Casa Hernández, Jesús; Aguilar-Peña, Juan Domingo
Most of the studies that can be found in the literature for analysing self-consumption systems with storage focus on global self-consumption and self-sufficiency indices and it may be very difficult to define the role of the array power and battery. In this sense, a new approach to analysing this type of systems is provided where direct and battery self-sufficiency and self-consumption indices are defined. The latter represent the direct photovoltaic self-consumed energy and the one provided by the battery. New direct and battery ZEB points are also presented. Furthermore, this type of system is generally analysed using complex 3D plots. Therefore, a new and intuitive 2D contour tool is provided: the iso selfconsumption curves. The new approach has been applied to three households located in Spain. Results show that it may be reached a global self-sufficiency of 50% considering array powers and rated capacities below 3.5 kWp and 1 kWh, respectively, where direct and battery self-sufficiency indices may reach 40% and 10%, respectively. This new method together with the graphical tool may help not only to analyse this type of system but to properly size the array power and the rated capacity from either an energetic or profitability approach.
A Novel Family of Efficient Power-Flow Methods With High Convergence Rate Suitable for Large Realistic Power Systems
(IEEE, 2021-03) Tostado-Véliz, Marcos; Kamel, Salah; Jurado-Melguizo, Francisco
High-order power-flow (PF) solution methods are techniques with higher convergence rate than the standard Newton-Raphson (NR). This feature normally provokes that less iterations are necessary for achieving the required convergence tolerance. This advantage enables important computational savings in realistic large-scale power systems, since some expensive computations may be avoided. This article develops and analyzes a novel family of multistep PF solution techniques. The introduced solution paradigm just involves an LU decomposition along with other cheap computations each iteration. In addition, it is proved that its convergence order is equal to the number of steps considered. A comparison with other high-order PF techniques available in the literature reveals that the introduced paradigm is more efficient when more than three steps are taken. Hence, two PF methods with fourth and fifth convergence rate are developed and validated in 12 systems under different demand conditions. Results prove that the developed PF solution methods are able to notably outperform NR and the other high-order PF solvers proposed in the literature.
A novel hybrid lexicographic-IGDT methodology for robust multi-objective solution of home energy management systems
(Elsevier, 2022-08-15) Tostado-Véliz, Marcos; Kamel, Salah; Aymen, Flah; Jurado-Melguizo, Francisco
With the emergence of smart appliances and communication infrastructures, Home Energy Management Systems have gained importance to help home users to reduce their electricity bills. A Home Energy Management System is a tool able to optimally coordinate the different home assets such as controllable appliances, onsite generators and storage facilities, among others. Such kind of tools has become more complex with the appearance of dynamic pricing tariffs and novel appliances such as electric vehicles. In this context, scheduling tools must attain a high level of robustness against uncertainties as well as being able to consider the particular behaviour of unpredictable energy pricing and vehicle routines, while some complementary objectives like thermal comfort are not ignored. This paper addresses this issue by developing a novel hybrid robust-multi objective home energy management approach. The novel proposal is based on information gap decision theory and lexicographic optimization, which are combined in an original way to attain a scheduling plan immune against the negative effect of uncertainties, while the economy and comfort of the building are jointly considered. The developed mathematical formulation is Mixed Integer Linear Programming, employing advanced linearization techniques to overcome the problems arisen from nonlinear models. Its particular integer-linear structure makes the developed optimization problem easily tractable by conventional solvers and average machines. Also, further capabilities are explored such as the possibility of selling energy to the grid and the vehicle-to-home ability of electric vehicles. Extensive simulations are performed on a benchmark prosumer environment considering real time pricing and time-of-use tariffs. The result serves to prove that the developed methodology is able to deal with uncertainties whereas different objective functions are jointly accounted.
A novel interval-based formulation for optimal scheduling of microgrids with pumped-hydro and battery energy storage under uncertainty
(Wiley, 2022-05-06) Ahmadi, Saeid; Tostado-Véliz, Marcos; Ghadimi, Ali Asghar; Miveh, Mohammad Reza; Jurado, Francisco
Nowadays, microgrids are emerging as an invaluable framework for the integration of renewable energy sources and demand response programs. In such systems, energy storage facilities are also frequently deployed to properly manage surplus energy from renewable sources on pursuing more efficient management of the system. Hybrid storage systems in which various storage facilities are combined may result in a more effective solution than only considering one storage technology. This way, the good features of the different technologies may be jointly exploited while their drawbacks are minimized. Due to the large-scale integration of renewable energies in this kind of grid, coping with uncertainties becomes a critical issue. Moreover, the operation of microgrids frequently deals with other kinds of uncertainties related to energy pricing from the upscale grid (in the case of grid-connected mode) or local demand. This way, proper modeling of uncertainties is essential for adequately operating these systems. This paper contributes to this pool by developing a novel interval-based formulation, for optimal scheduling of microgrids considering battery and pumped-hydro storage systems. To achieve this goal, the optimal scheduling of a microgrid with pumped-hydro and battery energy storage considering demand response is modeled, firstly. Then, the new interval-based formulation is used to cope with the uncertainties. Finally, the suggested model is verified using simulations in various cases, and the results confirm the effectiveness of the novel interval-based formulation for the optimal scheduling of microgrid with pumped-hydro and battery energy storage under uncertainty.
A novel methodology for comprehensive planning of battery storage systems
(Elsevier, 2021-05) Arévalo, Paul; Tostado-Véliz, Marcos; Jurado-Melguizo, Francisco
Battery storage system design has become a crucial task for nanogrids and microgrids planning, as it strongly determines the techno-economic viability of the project. Despite that, most of developed methodologies for optimally planning this kind of systems still present some important issues like high computational burden or insufficient results. This paper develops a novel methodology for battery storage system planning in nanogrids and microgrdis, which aims at overcoming the main issues presented by other methodologies. To achieve this goal, our proposal originally combines different software, clustering techniques and optimization tools. As salient features of the developed approach, it is worth remarking its efficiency, versatility, ability to manage with different time horizons and comprehensiveness. A prospective nanogrid in the region of Cuenca, Ecuador, serves as illustrative case study to show the capabilities, efficiency and effectiveness of the proposed approach as providing sufficient guidelines for its universal applicability. Among other relevant results, our proposal is able to determine that, for the studied grid, the daily operating cost can be reduced up to 17% by using Nickel-Cadmium batteries, however, the usage of Lead-Acid and Sodium-Sulfur technologies resulted more attractive through the project lifetime due to their longer lifetimes and relatively low capital costs.
A novel methodology for optimal sizing photovoltaic-battery systems in smart homes considering grid outages and demand response
(Elsevier, 2021-06) Tostado-Véliz, Marcos; Icaza-Alvarez, Daniel; Jurado-Melguizo, Francisco
This paper deals with the optimal sizing of a hybrid photovoltaic-battery storage system for home energy management considering reliability against grid outages and demand response. To that end, a novel optimization framework is developed which aims at minimizing the electricity bill while the reliability of the system is ensured for certain common outages. In order to ensure the accuracy of the results, a large amount of characteristic outages along with demand, solar irradiance and temperature profiles are generated from real data. Clustering techniques are used for reducing this data to those most characteristics profiles and manage with the unpredictable behaviour of the outage events. Demand response is incorporated via different incentives like tariffs based on time of use and real time pricing, along with the optimal scheduling of different typical deferrable appliances. A case study on a smart-prosumer environment serves to illustrate the capabilities of the developed approach as providing sufficient guidelines for its universal applicability. Different cases studies are simulated considering different battery technologies and electricity tariffs for comparison. Various aspects related with the reliability against grid outages are also analysed like its impact on the project cost or the influence of demand response strategies.
A novel Newton-like method with high convergence rate for efficient power-flow solution in isolated microgrids
(Wiley, 2023-03) Tostado-Véliz, Marcos; Bayat, Mohammad; Ghadimi, Ali Asghar; Jurado-Melguizo, Francisco
Power-Flow (PF) solution in isolated microgrids has attracted notable attention recently, because these systems present various particularities compared with the traditional PF solution in large meshed transmission networks. In this sense, this paper develops a novel Newton-like PF solver for isolated microgrids. The new proposal is based on the Modified Midpoint method and shows high convergence order with relatively low computational burden. These characteristics bring superior theoretical performance compared with the standard Newton–Raphson (NR) method and other high order techniques, which has been conventionally used. Extensive simulations are performed on various small-, and large-scale benchmark Microgrids under different loading conditions and R/X ratios. Results provided serve to confirm the theoretical features of the developed solver, outperforming the NR technique as well as other recently developed solvers in all the studied systems with acceptable reliability even under high stressed conditions.
A Novel Power Flow Solution Paradigm for Well and Ill-Conditioned Cases
(IEEE, 2021-08) Tostado-Véliz, Marcos; Alharbi, Talal; Alrumayh, Omar; Kamel, Salah; Jurado-Melguizo, Francisco
This paper develops a novel four-stage power flow solver for ill-conditioned systems. Although the developed solver could be considered efficient, it is not competitive with the Newton-Raphson method in well-conditioned cases. With the aim of being fully competitive in a wide range of cases and scenarios, the developed algorithm is integrated within a novel efficient solution paradigm. As a result, a robust and efficient solution framework, competitive in both well and ill-conditioned cases, is obtained. The new proposals are tested in various well and ill-conditioned cases from 30-, to 13,659-buses. Results obtained with the developed solvers are promising.

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